As Adrian says, 99.99% sure it's the F125 switch. Had this issue on mine (all gears lit up on display) before I knew what the issue was. Personally, I'd spend the £110 on a switch from the forum sponsors and then sell it fully working. You'll get more interest than for a car with a dodgy gearbox. If it's as good as you say with all the work done on it, you should be able to get much more for it. There is a '97 S8 on Pistonheads for £2,450.
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2001 A8 D2 FL 3.7 Q - LPG Conversion, Engine: AKC, Gearbox:FBB, Colour:LY5X Aqua Blue pearl effect, Interior:WJ light beige/dark beige valcona leather with burr walnut inserts
My DIY jobs - Replaced alarm horn, Replaced Coolant Temp sensor, Updated RNS-D firmware, Installed Reversing Camera and Digital TV, Dashcam Installation, Retrofitted Rear Blinds, Auto-Dimming Rear View Mirror, Chrome Boot Struts
Sold!  2008 S8 D3 5.2 V10 - Engine: BSM, Gearbox:KLW, Colour:LY7F Suzuka Grey Pearl Effect, Interior:Black/Black with Silver/Black valcona leather with carbon atlas inserts, Bang & Olufsen, Heated windscreen, Soft-close doors, TV, DAB, AMI, Quad Zone, Auto Boot, Auto dim Mirrors, Keyless entry, PDC with rearview camera, AFS II Headlights
My DIY jobs - Fan Jet Windscreen Washers, Retrofitted Electric Side Blinds
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